Being resourceful

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

How many moves does it take to swap over some red and blue frogs? Do you have a method?

Which set of numbers that add to 100 have the largest product?

In how many ways can you fit all three pieces together to make shapes with line symmetry?

How many different symmetrical shapes can you make by shading triangles or squares?

What do you notice about the sum of two identical triangular numbers?

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

Draw some isosceles triangles with an area of $9cm^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Can you find triangles on a 9-point circle? Can you work out their angles?